Origin and Compensation of GLONASS Inter-frequency Carrier Phase Biases in GNSS Receivers

It is well known that centimeter-level inter-frequency biases are a major source of problems for the GLONASS carrier phase ambiguity resolution. As already postulated by much research, these biases depend linearly upon the frequency number, change very little with time and temperature, and are almost equal for L1 and L2 bands when they are expressed in units of length. Although the general properties of the GLONASS inter-frequency carrier phase biases are well studied, their origin in the receiver processing chain has remained largely unexplained. It is typically assumed that the biases are generated in the analog hardware of receivers, and hence are difficult to tackle without specialized laboratory equipment. This paper presents an analysis of the possible sources of inter-frequency carrier phase biases in GNSS receivers and proposes a theory which explains all actually observed characteristics of the biases, in particular their linearity, stability and equal values for L1 and L2. The paper begins with the analysis of inter-frequency carrier phase biases generated in the analog hardware. It is shown that these are too small and cannot account for the observed centimeter-level values. Next, we proceed to the DSP section and show that the major cause of linear inter-frequency carrier phase biases is a difference in the receiver clock bias term applicable to code and carrier phase measurements, the so called “code-phase bias”. We identify two specific causes of code-phase biases in the DSP. First, it is a common practice to adjust code measurements by some constant offset in the receiver firmware. If this is done without corresponding adjustment to the carrier phase measurements, code-phase biases are created. The second cause of biases is found in the receiver’s digital signal processing chip, where reference code and phase signals may have different delays. It is shown that the DSP-induced code-phase biases are the primary cause of inter-frequency biases in GLONASS RTK. Being caused by digital processing and firmware, they are perfectly stable in time, do not change with temperature, and do not vary from unit to unit. It is also shown that, if the values of the code-phase biases are known, carrier phase measurements can be corrected for the most significant portion of the inter-frequency biases, which significantly simplifies GLONASS RTK operation.